Active Learning the Coarse-Grained Energy Landscape For Water Clusters From Sparse Training Data

ANNs are currently trained by generating large quantities (On the order of $10^{4}$ or greater) of structural data in hopes that the ANN has adequately sampled the energy landscape both near and far-from-equilibrium. This can, however, be a bit prohibitive when it comes to more accurate levels of quantum theory. As such it is desirable to train a model using the absolute minimal data set possible, especially when costs of high-fidelity calculations such as CCSD and QMC are high. Here, we present an Active Learning approach that iteratively trains an ANN model to faithfully replicate the coarse-grained energy surface of water clusters using only 426 total structures in its training data. Our active learning workflow starts with a sparse training dataset which is continually updated via a Monte Carlo scheme that sparsely queries the energy landscape and tests the network performance. Next, the network is retrained with an updated training set that includes failed configurations/energies from previous iteration until convergence is attained. Once trained, we generate an extensive test set of ~100,000 configurations sampled across clusters ranging from 1 to 200 molecules and demonstrate that the trained network adequately reproduces the energies (within mean absolute error (MAE) of ~ 2 meV/molecule) and forces (MAE ~ 40 meV/{\r{A}}) compared to the reference model. More importantly, the trained ANN model also accurately captures both the structure as well as the free energy as a function of the various cluster sizes. Overall, this study reports a new active learning scheme with promising strategy to develop accurate force-fields for molecular simulations using extremely sparse training data sets.